1999/03/31 by Yaw-Hwang Chen, Hai-Yang Cheng, B. Tseng +1 · 6 citations
Mathematics · Physics and Astronomy · #Algorithm #B meson #Combinatorics #Factorization #Hadron #Mathematics #Meson #Nuclear physics research studies #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Tree (set theory) #hep-ex #hep-ph
paper · pdf · doi:10.1103/physrevd.60.094014
published as Phys. Rev. D 60, 094014 (1999) · 72 pages, 14 figures. Data are updated; new discussions are added to sec.2. To appear in Phys. Rev
arxiv created 1999/07/03 · openalex publication_date 1999/10/08 · openalex created_date 2016/06/24 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
Two-body charmless nonleptonic decays of Bu and Bd mesons are studied within the framework of generalized factorization in which the effective Wilson coefficients cieff are renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Contrary to previous studies, our cieff do not suffer from gauge and infrared problems. Nonfactorizable effects are parametrized in terms of Nceff(LL) and Nceff(LR), the effective numbers of colors arising from (V\ensuremath-A)(V\ensuremath-A) and (V\ensuremath-A)(V+A) four-quark operators, respectively. Tree and penguin transitions are classified into six different classes. The data of B^\ensuremath-\ensuremath→\ensuremathρ0\ensuremathπ^\ensuremath- and B^\ensuremath-\ensuremath→\ensuremathφK^\ensuremath- clearly indicate that Nceff(LR)\ensuremath≠Nceff(LL): The first measurement of the \stackrel\ensuremath→bu mode B^\ensuremath-\ensuremath→\ensuremathρ0\ensuremathπ^\ensuremath- and the experimental information on the tree-dominated mode B^\ensuremath-\ensuremath→\ensuremathω\ensuremathπ^\ensuremath- all imply that Nceff(LL) is less than 3, whereas the CLEO measurement of B^\ensuremath-\ensuremath→\ensuremathφK^\ensuremath- shows Nceff(LR)>3. For given input parameters, the prediction of B(\stackrel\ensuremath→B\ensuremathη^\ensuremath'K) is largely improved by setting Nceff(LL)\ensuremath∼2 and Nceff(LR)>Nceff(LL); in particular, the charm content of the \ensuremathη^\ensuremath' contributes in the right direction. The decay rate of \stackrel\ensuremath→B\ensuremathφK* is very sensitive to the form-factor ratio A2/A1; the absence of \stackrel\ensuremath→B\ensuremathφK events does not necessarily invalidate the factorization approach. If the branching ratio of B^\ensuremath-\ensuremath→\ensuremathωK^\ensuremath- is experimentally found to be significantly larger than that of B^\ensuremath-\ensuremath→\ensuremathρ0K^\ensuremath-, we argue that inelastic final-state rescattering may account for the disparity between \ensuremathωK^\ensuremath- and \ensuremathρ0K^\ensuremath-. By contrast, if B(B^\ensuremath-\ensuremath→\ensuremathρ0K^\ensuremath-)\ensuremath∼B(B^\ensuremath-\ensuremath→\ensuremathωK^\ensuremath-) is observed, then W annihilation and/or spacelike penguin amplitudes could play a prominent role. The decay modes Bd0\ensuremath→\ensuremathφ\ensuremathπ0,\ensuremathφ\ensuremathη,\ensuremathφ\ensuremathη^\ensuremath',\ensuremathφ\ensuremathρ0,\ensuremathφ\ensuremathω,B^\ensuremath-\ensuremath→\ensuremathφ\ensuremathπ^\ensuremath-,\ensuremathφ\ensuremathρ^\ensuremath- involving a vector meson \ensuremathφ are dominated by electroweak penguin amplitudes. We show that a unitarity angle \ensuremathγ larger than 90\ifmmode^∘\else\textdegree\fi is helpful for explaining the \ensuremathπ+\ensuremathπ^\ensuremath-, \ensuremathπK, and \ensuremathη^\ensuremath'K data. The relative magnitudes of tree, QCD penguin, and electroweak penguin amplitudes are tabulated for all charmless \stackrel\ensuremath→BPP,VP,VV decays. Our favored predictions for branching ratios are those for Nceff(LL)\ensuremath≈2 and Nceff(LR)\ensuremath∼5.